Violation of Bell's inequality with photons from independent sources

We report a violation of Bell's inequality using one photon from a parametric down-conversion source and a second photon from an attenuated laser beam. The two photons were entangled at a beam splitter using the postselection technique of Shih and Alley [Phys. Rev. Lett. 61, 2921 (1988)]]. A quantum interference pattern with a visibility of 91% was obtained using the photons from these independent sources, as compared with a visibility of 99.4% using two photons from a central parametric down-conversion source.     

Bell's inequality for a single particle

Bell's inequality must be satisfied by a theory that can be based on local realistic variables. We derive such an inequality and show that it is violated by some quantum mechanical states. These states may be looked upon as pertaining to one particle.This paper is a contribution in honor of Prof. M. Jammer's 80th birthday April 13, 1995.     

Proposal for a loophole-free Bell test using homodyne detection

We propose a feasible optical setup allowing for a loophole-free Bell test with efficient homodyne detection. A non-Gaussian entangled state is generated from a two-mode squeezed vacuum by subtracting a single photon from each mode, using beam splitters and standard low-efficiency single-photon detectors. A Bell violation exceeding 1% is achievable with 6 dB squeezed light and a homodyne efficiency around 95%. A detailed feasibility analysis, based upon the recent experimental generation of single-mode non-Gaussian states, suggests that this method opens a promising avenue towards a complete experimental Bell test.     

Effective quantum efficiency in the pulsed homodyne detection of a n-photon state

Homodyne detection can be used to perform measurements on various quantum states of the light, such as conditional single photon states produced by parametric fluorescence processes. In the pulsed regime, the time and frequency overlap between the single photon wave packet and the local oscillator field plays a crucial role. We show in this paper that this overlap can be characterized by an effective quantum efficiency, which is explicitly calculated in various situations of experimental interest. Received 27 July 2000 and Received in final form 29 November 2000     

Multilayer optical disc system using homodyne detection

A write/read system using high-productivity multilayer optical discs was developed. The recording medium used in the system consists of planar recording layers and a separated guide layer, and is fabricated by web coating and lamination process. The recording layers in the medium are made of one-photon-absorption material, on which data can be recorded with a normal laser diode. The developed system is capable of focusing and tracking on the medium and amplifying readout signals by using phase-diversity homodyne detection. A highly layer-selective focusing method using homodyne detection was also proposed. This method obtains stable focus-error signals with clearly separated S-shaped curves even when layer spacing is quite narrow, causing large interlayer crosstalk. Writing on the medium and reading with the signal amplification effect of homodyne detection was demonstrated. In addition, the effectiveness of the method was experimentally evaluated.     

Entanglement in 2DEG systems: towards a detection loophole-free test of Bell's inequality

We make use of the intrinsic noiseless and lossless aspect of an electron source in a 2DEG system to implement a new test of Bell's inequality. The generated entanglement can be tested by two-particle interferometry. Preparation and detection schemes of two complete sets of Bell states are given. A novel type of Bell's inequality is then derived in terms of noise correlation measurements. The characteristics of the electron source are essential to exhibit a violation. This electron system could close the detection efficiency loophole.     

Quantum generalizations of Bell's inequality

Even though quantum correlations violate Bell's inequality, they satisfy weaker inequalities of a similar type. Some particular inequalities of this kind are proved here. The more general case of instruments located in different space-time regions is also discussed in some detail.     

Relativistic invariance of Bell's inequality

Based on a simple argument of relativistic covariance, I argue that the correlation between the polarization states of entangled photons, as predicted by quantum mechanics, is Lorentz invariant. Therefore, Bell's inequality for polarization states cannot be affected by the motion of detectors.     

Quantum homodyne tomography of a two-photon Fock state

We present a continuous-variable experimental analysis of a two-photon Fock state of free-propagating light. This state is obtained from a pulsed nondegenerate parametric amplifier, which produces two intensity-correlated twin beams. Counting two photons in one beam projects the other beam in the desired two-photon Fock state, which is analyzed by using a pulsed homodyne detection. The Wigner function of the measured state is clearly negative. We developed a detailed analytic model which allows a fast and efficient analysis of the experimental results.     

Has Bell's inequality a general meaning for hidden-variable theories?

We analyze the proof given by J. S. Bell of an inequality between mean values of measurement results which, according to him, would be characteristic of any local hidden-parameter theory. It is shown that Bell's proof is based upon a hypothesis already contained in von Neumann's famous theorem: It consists in the admission that hidden values of parameters must obey the same statistical laws as observed values. This hypothesis contradicts in advance well-known and certainly correct statistical relations in measurement results: One must therefore reject the type of theory considered by Bell, and his inequality has no general meaning.     

Violation of Locality Beyond Bell's Theorem for Multiparticle Perfect Correlations

We present the analogous inequalities of Bell's inequality for N-qubit system predicted respectively by realistic theory, quantum mechanics, local theory, local realistic theory, and local quantum theory on the same Bell-type joint experiment. It is shown that quantum mechanics can be interpreted by hidden-variable theories while being incompatible to any local theory. A necessary condition for the separability of N-qubit system is derived.     

Quantum state sharing of an arbitrary qudit state by using nonmaximally generalized GHZ state

We present a scheme for quantum state sharing of an arbitrary qudit state by using nonmaximally entangled generalized Greenberger-Horne-Zeilinger （GHZ） states as the quantum channel and generalized Bell-basis states as the joint measurement basis. We show that the probability of successful sharing an unknown qudit state depends on the joint measurements chosen by Alice. We also give an expression for the maximally probability of this scheme.     

从贝尔不等式到量子信息"热"

介绍了贝尔不等式的建立及20世纪70年代以来对它的实验验证．对贝尔不等式与量子力学基本解释的关系的深入研究,加速了“纠缠态”及其品性的发现,推动了量子信息“热”的兴起。     

Experimental violation of Bell's inequality in spatial-parity space

We report the first experimental violation of Bell's inequality in the spatial domain using the Einstein-Podolsky-Rosen state. Two-photon states generated via optical spontaneous parametric down-conversion are shown to be entangled in the parity of their one-dimensional transverse spatial profile. Superpositions of Bell states are prepared by manipulation of the optical pump's transverse spatial parity-a classical parameter. The Bell-operator measurements are made possible by devising simple optical arrangements that perform rotations in the one-dimensional spatial-parity space of each photon of an entangled pair and projective measurements onto a basis of even-odd functions. A Bell-operator value of 2.389+/-0.016 is recorded, a violation of the inequality by more than 24 standard deviations.     

Experimental violation of Bell's inequality beyond Tsirelson's bound

The correlations between two qubits belonging to a three-qubit system can violate the Clauser-Horne-Shimony-Holt-Bell inequality beyond Tsirelson's bound [A. Cabello, Phys. Rev. Lett. 88, 060403 (2002)]. We experimentally demonstrate such a violation by 7 standard deviations by using a three-photon polarization-entangled Greenberger-Horne-Zeilinger state produced by Type-II spontaneous parametric down-conversion. In addition, using part of our results, we obtain a violation of the Mermin inequality by 39 standard deviations.     

Strong violations of locality by testing Bell's inequality with improved entangled-photon systems

Bell's theorem states that quantum mechanics cannot be accounted for by any local theory. One of the examples is the existence of quantum non-locality is essentially violated by the local Bell's inequality. Therefore, the violation of Bell's inequality(BI) has been regarded as one of the robust evidences of quantum mechanics. Until now, BI has been tested by many experiments, but the maximal violation(i.e., Cirel'son limit) has never been achieved. By improving the design of entangled sources and optimizing the measurement settings, in this work we report the stronger violations of the Clauser–Horne–Shimony–Holt(CHSH)-type Bell's inequality. The biggest value of Bell's function in our experiment reaches √to a significant one: S = 2.772 ± 0.063, approaching to the so-called Cirel'son limit in which the Bell function value is S = 22.Further improvement is possible by optimizing the entangled-photon sources.